Simplify (6+5i)(6-5i)

$(6 + 5 i) (6 - 5 i)$

Step 1

Expand $(6 + 5 i) (6 - 5 i)$ using the FOIL Method.

Apply the distributive property.

$6 (6 - 5 i) + 5 i (6 - 5 i)$

Apply the distributive property.

$6 \cdot 6 + 6 (- 5 i) + 5 i (6 - 5 i)$

Apply the distributive property.

$6 \cdot 6 + 6 (- 5 i) + 5 i \cdot 6 + 5 i (- 5 i)$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $6$ by $6$ .

$36 + 6 (- 5 i) + 5 i \cdot 6 + 5 i (- 5 i)$

Multiply $- 5$ by $6$ .

$36 - 30 i + 5 i \cdot 6 + 5 i (- 5 i)$

Multiply $6$ by $5$ .

$36 - 30 i + 30 i + 5 i (- 5 i)$

Multiply $5 i (- 5 i)$ .

Multiply $- 5$ by $5$ .

$36 - 30 i + 30 i - 25 i i$

Raise $i$ to the power of $1$ .

$36 - 30 i + 30 i - 25 (i^{1} i)$

Raise $i$ to the power of $1$ .

$36 - 30 i + 30 i - 25 (i^{1} i^{1})$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$36 - 30 i + 30 i - 25 i^{1 + 1}$

Add $1$ and $1$ .

$36 - 30 i + 30 i - 25 i^{2}$

Rewrite $i^{2}$ as $- 1$ .

$36 - 30 i + 30 i - 25 \cdot - 1$

Multiply $- 25$ by $- 1$ .

$36 - 30 i + 30 i + 25$

Add $36$ and $25$ .

$61 - 30 i + 30 i$

Add $- 30 i$ and $30 i$ .

$61 + 0$

Add $61$ and $0$ .

$61$